Guillaume Dauphinais

We present a framework where the inherent physical imperfections of Gottesman-Kitaev-Preskill (GKP) states—specifically the finite-energy envelopes required for normalizability—are harnessed as a resource for universal quantum computation. Contrary to the standard view that treats the finite squeezing of GKP states solely as a source of error to be corrected, we demonstrate that ``Fock damping'' enables the implementation of non-Clifford gates using only Gaussian operations and homodyne detection. We prove a dichotomy: while ideal (infinite energy) stabilizer GKP states are restricted to Clifford operations under Gaussian operation and measurement, realistic (finite energy) states allow for projection onto non-Pauli eigenstates, including magic states. At experimentally realistic squeezing levels, our protocol yields magic states with fidelities sufficient for distillation with success probabilities exceeding 40\%. This resolves an open question regarding the universality of realistic GKP circuits without requiring auxiliary vacuum modes or resource greedy GKP error correction.